We keep the position of start, checkpoints considering a free-order race. The only difference of the free order of visit of the checkpoints requires a much larger number of states. The set \({\mathcal {I}}\)  is composed by all the possible permutations with repetitions of the elements \(\lbrace 0,1\rbrace \)  on a 7-elements vector. Therefore, the total number of the discrete states rises to \(2^m=128\) , bringing the number of nodes in the discrete space to \(3\cdot 10^7\) . This fact, together with the number of fixed point iterations necessary to reconstruct the solution, requires a certain care from the point of view of the computational efficiency. In any case, our code, implemented in Matlab2019b on a 1,4 GHz Quad-Core Intel Core i5 processor, reaches the solution under a prescribed tolerance of \(10^{-3}\)  on the uniform norm in about 20 hours of computations. If more effective performances are needed, a viable strategy would be to adapt a fast marching technique in this case (see the classic book by [1]} for details).
